Difference between revisions of "Team:Tec-Monterrey/Model"

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       Specifically, answering questions as why, how, when, what, regarding our biological system is our objective.
 
       Specifically, answering questions as why, how, when, what, regarding our biological system is our objective.
 
     </section>
 
     </section>
     <section id="introduction-model" class="seccion-responsiva">
+
 
      The modeling of the system was approached through a progressive development of the model. The first model that was proposed consisted on a simple linear differential equation system based on mass-reaction laws of kinetics to describe the interaction of genetic material and the dependence of the productions of each genetic material with the concentrations of the other relevant genetic materials. That is, the various interactions that the compounds have are considered, and for each compound, these interactions define the shape of the differential equation that describes it. The most relevant information to model is the concentration of the CAS complex annexed to the to-be-inserted genetic information. The concentration of this compound is proportional to the probability that the genetic material is inserted into the bacterium, a binomial distribution was considered to describe the probability density function that portrays the behavior of the insertion system. <br>
+
     <section id="module1&2-model" class="seccion-responsiva">
     </section>
+
    <div class="contenido">
 +
        <div class="body-title">Module 1 & Module 2</div>
 +
        <div class="body-subtitle">Protein and target DNA production</div>
 +
        In beginning with a mathematical description of the E. coding system, the biomolecular processes taking place in the system were expressed as reversible biochemical reactions governed by mass-action law kinetics, as conveyed in Figure ***.
 +
    <div class="imagen-centrada-completa">
 +
        <img src="https://static.igem.org/mediawiki/2018/b/b0/T--Tec-Monterrey--MODEL_DIAGRAMA.png">
 +
      </div>
 +
        Where Cas1 refers to free Cas1 protein, Cas2 to free Cas2 protein, RT to free Retrotranscriptase, msr-msd to free msr-msd RNA transcript, CAS to free Cas1-Cas2 protein complex, M to RT bound by msr-msd RNA transcript, MSD to free retrotranscribed target DNA sequence, X to Cas1-Cas2 protein complex bound to target DNA sequence, and I to the amount of insertions made to the bacteria’s genome. This first model consisted of a simple linear differential equations system.
 +
The initial principle of the system is the expression of three proteins (Cas1, Cas2, and a Retrotranscriptase) and the msr-msd RNA transcript, regulated by an inducible promoter. As such, the Hill equation was implemented to describe said regulated expression, as a function of the concentration of an inductor. A separate term, for basal protein degradation remained. Additionally, enzymatic processes, such as protein complex formation, substrate binding, or enzymatic reactions, are left described by mass-action law. Equations *** to *** correspond to each protein, substrate, and enzymatic complex involved in the E. coding system.
 +
 
 +
Equation 1
 +
Equation 2
 +
Equation 3
 +
Equation 4
 +
Equation 5
 +
Equation 6
 +
Equation 7
 +
 
 +
Through steady-state assumptions, the system of equations was further reduced:
 +
= 0
 +
 
 +
Substituting, Equation *** in Equation ***, and Equation *** in Equation ***, a single expression for the amount of target DNA sequence is defined as:
 +
Equation ***
 +
 
 +
        <div class="body-subtitle">Genomic Spacer acquisition</div>
 +
 
 +
     </div>
 +
</section>
 +
 
 
     <section id="reaction-mech" class="seccion-responsiva">
 
     <section id="reaction-mech" class="seccion-responsiva">
 
       A diagram encompassing the various biological interactions, as well as how and when they combine and transform, between all the interest compounds is as follows:<br>
 
       A diagram encompassing the various biological interactions, as well as how and when they combine and transform, between all the interest compounds is as follows:<br>

Revision as of 22:18, 15 October 2018

Test 1
Test 2
For the entirety of human history, information gathering and storing has been of huge interest to society. One of the most, important aspects of information is the capability of that information to be gathered, stored, read, and analyzed.
The role of the mathematical model is explaining this and discovering particularities about the specifics of information, so that processes involving information are made better. Specifically, answering questions as why, how, when, what, regarding our biological system is our objective.
Module 1 & Module 2
Protein and target DNA production
In beginning with a mathematical description of the E. coding system, the biomolecular processes taking place in the system were expressed as reversible biochemical reactions governed by mass-action law kinetics, as conveyed in Figure ***.
Where Cas1 refers to free Cas1 protein, Cas2 to free Cas2 protein, RT to free Retrotranscriptase, msr-msd to free msr-msd RNA transcript, CAS to free Cas1-Cas2 protein complex, M to RT bound by msr-msd RNA transcript, MSD to free retrotranscribed target DNA sequence, X to Cas1-Cas2 protein complex bound to target DNA sequence, and I to the amount of insertions made to the bacteria’s genome. This first model consisted of a simple linear differential equations system. The initial principle of the system is the expression of three proteins (Cas1, Cas2, and a Retrotranscriptase) and the msr-msd RNA transcript, regulated by an inducible promoter. As such, the Hill equation was implemented to describe said regulated expression, as a function of the concentration of an inductor. A separate term, for basal protein degradation remained. Additionally, enzymatic processes, such as protein complex formation, substrate binding, or enzymatic reactions, are left described by mass-action law. Equations *** to *** correspond to each protein, substrate, and enzymatic complex involved in the E. coding system. Equation 1 Equation 2 Equation 3 Equation 4 Equation 5 Equation 6 Equation 7 Through steady-state assumptions, the system of equations was further reduced: = 0 Substituting, Equation *** in Equation ***, and Equation *** in Equation ***, a single expression for the amount of target DNA sequence is defined as: Equation ***
Genomic Spacer acquisition
A diagram encompassing the various biological interactions, as well as how and when they combine and transform, between all the interest compounds is as follows:

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